Black or White Coffee which will cooldown first?

Pimp

Pimp

Captain of USS Defiant
Hello people.

The other day i was arguing with my brother (as one does) because he was telling me a scientific experiment that i didn't agree with:

There are two cups of coffee with the exact amount of liquid.

One of the cups contains just black coffee while the other contains coffee but with added milk (hence white coffee)

Now you leave the two cups of coffee for 5 minuets and then take a temperature reading.

Which one will be cooler??

I like any other person would say the white coffee will be cooler becuase you added milk which cools the coffee at start.

But what my brother said was that the black coffee will be cooler after 5 minuets because it has more heat (thermo energy) and therefore it will release more heat then the cooler white coffee which has less heat to start with. So at the end of the 5 minuets the black coffee would have released more energy and be cooler then the white.

That makes sense but i still don't see the black being cooler lol, BTW my bro has been offered a place at Cambridge University so he is kind of clever :doh:

what do you guys think?????

BTW you can't do this experiment at home because you need laboratory conditions to get accurate reading.
 
In this case, you are right. The coffee releases the same amount of thermal energy in both cups, but when you add the milk to one cup, you accelerate the cooldown process. You can test this very easy. Fill 2 buckets with hot water for about the half of the bucket. Now fill 1 bucket with cold water, and then see which bucket cools down first.
 
Pimp said:
Which one will be cooler??
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well, since the milk was added to one of the cups with the exact same amount of liquid as the other, the one with the milk actually contains more liquid from the begining of the test, this makes the test unfair & therefor void[ot]can anyone else think of a better answer[/ot]Edit: BTW: what was the starting temp of coffee & were the starting temp the same for both cups ?
 
donkey42 said:
well, since the milk was added to one of the cups with the exact same amount of liquid as the other, the one with the milk actually contains more liquid from the begining of the test, this makes the test unfair & therefor void[ot]can anyone else think of a better answer[/ot]Edit: BTW: what was the starting temp of coffee & were the starting temp the same for both cups ?
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No mate you got it wrong, what i meant was both cups contain the same amount of liquid including the milk, so: white= 10% milk / 90% water and black = 100% water (actually it would be 99.999% because you have to count the actual coffee)

I don't know the starting temp I'm guessing around 90c

also you have to take in consideration the temperature of milk and room temperature has to be constant. :doh:
 
Assuming constant room temperatures, according to Newton's law of cooling the rate at which the body cools is proportional to the difference in temperature between the body and surroundings.

Gonna go into calculus here but this can be described as:
dx/dt = -k(x - R)
where x is the temperature of the body, and R is surrounding temperature. k is a constant specific to the body.
So we can see that at higher temperatures (x) the rate of cooling is higher as expected, but that does not mean that after 5 minutes the black coffee is cooler. As the black coffee cools, the rate of change of temperature also decreases (x - R is lower). Both black and white coffee behave the same, they are just different stages of cooling with white coffee having cooled for longer.
 
trust you Addis
Addis said:
dx/dt = -k(x - R)
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& Swansen thinks i can over complcate stuff

now i'm really confused, tw4t[ot]joking[/ot]for me calculus is comparable to most women,
 
Pimp said:
donkey you joker
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i'm the joker ?

you found it funny[ot]ok, ok, ok, i did too[/ot]BTW: i haven't posted any pics for a while

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just a few to keep everyone quiet
 
haha funny pics but just one thing with the first pic i cant see it properly because it's too small but is someone putting a rubber johnny on the network?
 
Yeah I was gonna say the same thing Addis did, but the jerk beat me to it. :P

The one exception could possibly be if radiation is a big enough factor. Black coffee will radiate heat faster since it's black. Newton's law of cooling applies to heat loss by conduction, so perhaps the faster heat radation rate would allow the black coffee to pull ahead at some point (become colder) as they are both approaching room temperature. But that seems really unlikely.
 
DaRuSsIaMaN said:
Yeah I was gonna say the same thing Addis did, but the jerk beat me to it. :P

The one exception could possibly be if radiation is a big enough factor. Black coffee will radiate heat faster since it's black. Newton's law of cooling applies to heat loss by conduction, so perhaps the faster heat radation rate would allow the black coffee to pull ahead at some point (become colder) as they are both approaching room temperature. But that seems really unlikely.
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Not quite. Newton's law of cooling applies to convection, not conduction. Conduction is governed by Fourier's law which is similar but differs with the constant of proportionality.

Seems that Newton's law applies to body's cooling in a draft by forced convection, I don't know how much that applies to coffee cooling though.

You raise a good point about the colour, but I doubt it would affect it much. Plus a substantial amount of cooling will be done by the sides of the cup. Anyway back to work at 12:15am for my deadline in a few hours....:confused:
 
DR-man said:
but the jerk beat me to it
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who ?, me, thankies for the compliment, personally, i haven't being called that for years
Addis said:
You raise a good point about the colour, but I doubt it would affect it much. Plus a substantial amount of cooling will be done by the sides of the cup. Anyway back to work at 12:15am for my deadline in a few hours....
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:good:, i won't have to pretend i understand[ot]kidding Addis[/ot]
 
Ive heard this before but with buckets of hot and cold water placed in a freezer. The hot water freezes faster than the cold water for some scientific reason probably described somewhere above amongst the maths and algebra.
 
Yeah that's why your not meant to put hot foods in the fridge because it raises the temperature inside the fridge, which ain't really good for the rest of the food inside the fridge. Because the hot bucket will release more heat in the freezer then a cooler bucket would.

That might explain the black coffee cooling quicker.
 
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